Three-dimensional kinematics of saccadic eye movements in humans: is the "half-angle rule" obeyed?

The "half-angle rule" must be satisfied for Listing's law to be obeyed during saccades: the eye velocity axis must tilt away from Listing's plane by half the angle of eye position eccentricity from primary position. We aimed to determine if this rule is satisfied during saccades. Horizontal and vertical saccades were recorded using the search coil technique, at different elevations and azimuths, in five normal humans. In all, eye positions were located on a twisted rather than planar surface. The mean tilt-angle coefficients (TACs; ratio of angle of eye velocity axis tilt to angle of eye position eccentricity) were 0.57 and 0.34 for horizontal and vertical saccades, respectively. TACs were significantly lower for vertical saccades. Thus, Listing's law is not perfectly obeyed during saccades. We suggest that the discrepancy in horizontal and vertical TACs causes eye positions to lie on a twisted rather than planar surface in three-dimensional space.